When you have a correspondence where this remains true for all products, it's called an " isomorphism" , which is maybe the most important idea in group theory.

当你有一个对所有产品都成立对应关系时，它被称为“同构” ，这可能是群论中最要想法。

Vaida's treatment of the verbal morphology involves a tiny handful of intriguing isomorphisms, surrounded by an impenetrable sea of assumptions and highly controversial internal reconstructions that create an illusion of systemic reconstruction where there really is none.

Vaida 对词语形态理涉及极少数有趣同构，而这些同构周则充满了难以理解假设和极具争议建， 造成了一种系统建假象， 但实际上并不存在这种建。

This particular isomorphism between cube rotations and permutations of four objects is a bit subtle, but for the curious among you, you may enjoy taking a moment to think hard about how the rotations of a cube permute its four diagonals.

立方体旋转和四个对象排列之间这种特殊同构有点微妙，但对于好奇人来说， 您可能会喜欢花点时间认真思考立方体旋转如何排列其四个对角线。

But now you're in a position to ask that question in a more sophisticated way: What are all the groups up to isomorphism, which is to say we consider two groups to be the same if there's an isomorphism between them.

但现在你可以用更复杂方式问这个问题：所有群都达到同构程度是什么，也就是说，如果两个群之间存在同构，我们就认为它们是相同。